A steel compression member has effective length 2500 mm and least radius of gyration 20 mm. Slenderness ratio is

Why is this the answer?

Slenderness ratio lambda = Le / r, where Le = effective length (depends on end conditions: both ends pinned Le=L; one fixed one free Le=2L; etc.) and r = least radius of gyration = sqrt(I_min/A). IS 800:2007 limits: lambda <= 180 for compression members, <= 400 for tension. Higher lambda means greater tendency to buckle under compression (Euler critical load = pi^2*E*I/Le^2). Slenderness ratio = Le/r = 2500/20=125.

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